Question

Find the length of side xx in simplest radical form with a rational denominator.

30°
60°
x
4

Answer 1

The value of 'x' with rational denominator =

`(4 √(3) )/(3)`

Explanation:

cos =

`(adjacent \: side)/(hypotenuse)`

cos 30 =

`( √(3) )/(2)`

given triangle is a right- angled triangle.

from the triangle,

cost 30 =

`(adjacent \: side)/(hypotenuse) \: \: = \: (2)/(x)`

`( √(3) )/(2) \: = (2)/(x)`

√3x = 4

`x \: = \: (4)/( √(3) )`

Rationalising the denominator we get,

x =

`(4)/( √(3) ) * ( √(3) )/( √(3) )`

x =

`(4 √(3) )/(3)`

Therefore, the value of 'x' =

`(4 √(3) )/(3)`